A Finite Regime Analysis of Information Set Decoding Algorithms

Decoding of random linear block codes has been long exploited as a computationally hard problem on which it is possible to build secure asymmetric cryptosystems. In particular, both correcting an error-affected codeword, and deriving the error vector corresponding to a given syndrome were proven to...
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Gespeichert in:

Autor*in:	Marco Baldi [verfasserIn] Alessandro Barenghi [verfasserIn] Franco Chiaraluce [verfasserIn] Gerardo Pelosi [verfasserIn] Paolo Santini [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	asymmetric cryptosystems code-based cryptosystems information set decoding

Übergeordnetes Werk:	In: Algorithms - MDPI AG, 2008, 12(2019), 10, p 209
Übergeordnetes Werk:	volume:12 ; year:2019 ; number:10, p 209

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/a12100209

Katalog-ID:	DOAJ032742517

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authorswithroles_txt_mv	Marco Baldi @@aut@@ Alessandro Barenghi @@aut@@ Franco Chiaraluce @@aut@@ Gerardo Pelosi @@aut@@ Paolo Santini @@aut@@
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callnumber-first	T - Technology
author	Marco Baldi
spellingShingle	Marco Baldi misc T55.4-60.8 misc QA75.5-76.95 misc asymmetric cryptosystems misc code-based cryptosystems misc information set decoding misc Industrial engineering. Management engineering misc Electronic computers. Computer science A Finite Regime Analysis of Information Set Decoding Algorithms
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topic_title	T55.4-60.8 QA75.5-76.95 A Finite Regime Analysis of Information Set Decoding Algorithms asymmetric cryptosystems code-based cryptosystems information set decoding
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title_sort	finite regime analysis of information set decoding algorithms
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title_auth	A Finite Regime Analysis of Information Set Decoding Algorithms
abstract	Decoding of random linear block codes has been long exploited as a computationally hard problem on which it is possible to build secure asymmetric cryptosystems. In particular, both correcting an error-affected codeword, and deriving the error vector corresponding to a given syndrome were proven to be equally difficult tasks. Since the pioneering work of Eugene Prange in the early 1960s, a significant research effort has been put into finding more efficient methods to solve the random code decoding problem through a family of algorithms known as information set decoding. The obtained improvements effectively reduce the overall complexity, which was shown to decrease asymptotically at each optimization, while remaining substantially exponential in the number of errors to be either found or corrected. In this work, we provide a comprehensive survey of the information set decoding techniques, providing finite regime temporal and spatial complexities for them. We exploit these formulas to assess the effectiveness of the asymptotic speedups obtained by the improved information set decoding techniques when working with code parameters relevant for cryptographic purposes. We also delineate computational complexities taking into account the achievable speedup via quantum computers and similarly assess such speedups in the finite regime. To provide practical grounding to the choice of cryptographically relevant parameters, we employ as our validation suite the ones chosen by cryptosystems admitted to the second round of the ongoing standardization initiative promoted by the US National Institute of Standards and Technology.
abstractGer	Decoding of random linear block codes has been long exploited as a computationally hard problem on which it is possible to build secure asymmetric cryptosystems. In particular, both correcting an error-affected codeword, and deriving the error vector corresponding to a given syndrome were proven to be equally difficult tasks. Since the pioneering work of Eugene Prange in the early 1960s, a significant research effort has been put into finding more efficient methods to solve the random code decoding problem through a family of algorithms known as information set decoding. The obtained improvements effectively reduce the overall complexity, which was shown to decrease asymptotically at each optimization, while remaining substantially exponential in the number of errors to be either found or corrected. In this work, we provide a comprehensive survey of the information set decoding techniques, providing finite regime temporal and spatial complexities for them. We exploit these formulas to assess the effectiveness of the asymptotic speedups obtained by the improved information set decoding techniques when working with code parameters relevant for cryptographic purposes. We also delineate computational complexities taking into account the achievable speedup via quantum computers and similarly assess such speedups in the finite regime. To provide practical grounding to the choice of cryptographically relevant parameters, we employ as our validation suite the ones chosen by cryptosystems admitted to the second round of the ongoing standardization initiative promoted by the US National Institute of Standards and Technology.
abstract_unstemmed	Decoding of random linear block codes has been long exploited as a computationally hard problem on which it is possible to build secure asymmetric cryptosystems. In particular, both correcting an error-affected codeword, and deriving the error vector corresponding to a given syndrome were proven to be equally difficult tasks. Since the pioneering work of Eugene Prange in the early 1960s, a significant research effort has been put into finding more efficient methods to solve the random code decoding problem through a family of algorithms known as information set decoding. The obtained improvements effectively reduce the overall complexity, which was shown to decrease asymptotically at each optimization, while remaining substantially exponential in the number of errors to be either found or corrected. In this work, we provide a comprehensive survey of the information set decoding techniques, providing finite regime temporal and spatial complexities for them. We exploit these formulas to assess the effectiveness of the asymptotic speedups obtained by the improved information set decoding techniques when working with code parameters relevant for cryptographic purposes. We also delineate computational complexities taking into account the achievable speedup via quantum computers and similarly assess such speedups in the finite regime. To provide practical grounding to the choice of cryptographically relevant parameters, we employ as our validation suite the ones chosen by cryptosystems admitted to the second round of the ongoing standardization initiative promoted by the US National Institute of Standards and Technology.
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A Finite Regime Analysis of Information Set Decoding Algorithms

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